Advanced statistics.

Hello, in a recent conversation I came across an important point that has stuck in my mind, and I wondered what your opinions as poker players might be?

The conversation goes a little something like this -
If we have a deck of cards and randomly shuffled them, after the shuffle, the dealing order is set, what will be dealt, will be aligned to seat order relative to deal order. The odds of any seat being dealt pocket aces are 1/221 from a single deck of 52 cards.

If we have a second deck of cards, the odds of any seat receiving aces from a different shuffled random deck are still 1/221.

Up to yet this is simple probabilities without any confusion.

The more tricky part goes something like this,

If we have 1000 decks of cards randomly shuffled, and placed the decks side by side in a line, several of those decks will hold, after the shuffle, a set sequence of each deck, that contains aces in you seat order of distribution of the sequence.

saying this visual

(deck1)(deck2)(deck3) ETC...................(deck1000)

The conversation continued something like -
If you were dealt every hand with a new deck every time, in order of the line, left to right, you are guaranteed to receive aces from several of the decks in your seat, (comparing to tourney play and sitting out not having effect on the deal).

Ok, that is understandable and the sequence of the deck is set for each deck after the shuffle, if you are on the small blind and deck 100 has an ace top card, that is what you get (obviously unknowingly the value until you are dealt it).

Continued - If we add a second table, the distribution is now altered and no longer are you guaranteed the aces you were guaranteed before in your seat position.

Ok, that makes sense, a second table changes the deck order or deck number you will receive,

Instead of deck 1,2,3,4,5,6, in order , we now may get deck 1, 4, 6,7,9, dependent to how fast each table plays and needs a new deck.

This is the thought that stuck with me, like the aces are pre-set to order, so are 72 and all other hands. My thought is that if deck 1,4,6,7,9 have all got 72 in set sequence order for my seat, then I would be seriously stuffed.

The conversation did continue about multi-tables and coolers etc, but I think you will get the idea,

This post has been edited 1 time(s), it was last edited by GoOnCal1: 16.04.2015 03:56.

I think you may be confusing "If" with actual events.
Statistics is the study of real world events. Probability is the theoretical analysis.
Changing the randomness of randomly shuffled decks should not affect the probability of any outcome.
Hope that helps?

probability for getting aces is 1/221 per deck, if you draw from 1000 decks its highly likely that you will get aces at least once, but never guaranteed.
the probability for getting aces drawing from two decks is 1-(220/221)^2, which is ~0.9% (an improvement over 1/221 which is ~0.5%). you can solve inductively for any number of decks by changing ^2 to ^n

This post has been edited 1 time(s), it was last edited by shatteredaces: 16.04.2015 10:40.

Originally posted by Tomaloc
no i dont get the idea

probability for getting aces is 1/221 per deck, if you draw from 1000 decks its highly likely that you will get aces at least once, but never guaranteed.
the probability for getting aces drawing from two decks is 1-(220/221)^2, which is ~0.9% (an improvement over 1/221 which is ~0.5%). you can solve inductively for any number of decks by changing ^2 to ^n

A bit of a surprise that you do not understand it, it is very simple to understand what was said.

In short if we have 1000 decks of cards and shuffled each individual deck, on average in 1000 decks shuffled there will be AA aligned to your seat order 4 times for this example in a deck order,

add a random deck order and you have to choose a deck , your odds are now 4/1000 of picking the correct deck, therefore your odds of being dealt pocket aces from 1000 random choice decks is 4/1000.

This post has been edited 1 time(s), it was last edited by shatteredaces: 16.04.2015 11:38.

Originally posted by GoOnCal1
What happened to the 1000 decks?

I brought 1,000,000 decks into it , to bring the talk to a more relative comparison to the issue, and internet poker having millions of decks in an in-line stack.

These decks are randomly distributed to a table when the table needs a new hand. Pre-shuffled pre-set sequences. For example a roulette wheel was a good comparison to the mechanism of timing randomness.

We are not relying on the random shuffle, we are relying that by timing of the random deck we receive, has in the set sequence, in our seat position, the distribution set order of a good hand to our seat.

A comparison to roulette, spin 1,000,000 decks of cards, that on average will have approx 4524 pairs of aces in the set sequence, aligned to your seat distribution.

your odds are - 4524/1,000,000 of hitting a deck that aligns a good hand to your seat.

Originally posted by GoOnCal1
I think they use a random number generator and games are dealt from a single deck

They use a RNG that works correctly for the shuffle. Millions of decks are put into a shuffle server, shuffled and then placed in a line, then each table gets a new deck every hand. You can research this or ask any onlne site, they will provide this information.

if I had 100 different sequences of sets of numbers that were placed in a que system , the first sequence being the first from the line in distributing , the sequence distributed 10 numbers to five receivers on one outlet, and the same to another outlet, 2 numbers of the sequence to each individual receiver in a corresponding order.

In ten of the sequences, outlet one, receiver 3, would receive 5 numbers 5's if only number 1 outlet was in operation, and outlet 2 was dormant,

when we run the sequence a second time, outlet 2 is in operation, and the distribution ratio is defined by each individual receiver time of action on both outlets, making the sequence more random and not probabilities of the original sequence of outlet one, receiver 3, of receiving the 5, 5/100

So basically the distribution of the 100 sequences becomes time based distribution.

Am I correct in thinking that outlet one, receiver 3, the probabilities of now getting the 5, is now unaccountable?

a standard dice 1-6, has a 1/6 chance of any number per role

2 dice would have a 6^2 chance of rolling the same number

If I was betting on one dice , and you was betting on the other dice, each time we role we both have 1/6 chance of hitting our betted number.

However , your sequence of rolls would be bimodal different to my roles. Your's and my sequence would be dependent to each dice, and difference to each others sequence.

If we swapped dice, our probabilities remain 1/6, and even if we bet each others spin , our probabilities remain 1/6.

If you rolled number 1, and I bet against you hitting another 1, my probabilities are 1/6, where to you repeat the number one, your probabilities are now 6^2, or 36-1.

In the second game we change the rules, stacked in a que is already predefined roles and results of each dependent dice, a sequence dependent to each of us based on one dice, for every time an even number comes out, we win, for every time an odd number comes out we lose.

We see 100 numbers each, I win only 33% of my numbers, where you win 88% of your numbers,

Your sequence was a wining sequence for you, with a 2-1 chance of getting even , ready predefined by the stored sequence,

Now if you were to alternate between dice, you would then have a bimodal distribution, working off two sequences rather than one sequence, both sequences then becoming differential to the original sequence.

So instead of just a predetermined random luck, you are changing the sequence luck by timing of choice,

This post has been edited 1 time(s), it was last edited by GoOnCal1: 17.04.2015 00:09.

Ummm.....No

In probability theory "dice" are assumed to be completely random.

In any theory, it is generally assumed that if a proposition cannot put clearly in a sentence or two, it will be fallacious.

Refer to my original post, you appear suffering some confusion.

An example of a bimodal distribution might be the height of human adults, women would be expected to form a group mean slightly lower than that of men.

Probability theories can be tested with statistics, there are literally billions of data points publicly available, apart from a few rag tags, conspiracy proponents, and examples of clear criminal behaviour, no one is saying the distribution of cards is not random.

You need to let this go, or go to 60 minutes.

-@ Scotty, There is something wrong with the transporter, I am still here.

This post has been edited 1 time(s), it was last edited by shatteredaces: 17.04.2015 01:36.

Originally posted by GoOnCal1
Ummm.....No

In probability theory "dice" are assumed to be completely random.

In any theory, it is generally assumed that if a proposition cannot put clearly in a sentence or two, it will be fallacious.

Refer to my original post, you appear suffering some confusion.

An example of a bimodal distribution might be the height of human adults, women would be expected to form a group mean slightly lower than that of men.

Probability theories can be tested with statistics, there are literally billions of data points publicly available, apart from a few rag tags, conspiracy proponents, and examples of clear criminal behaviour, no one is saying the distribution of cards is not random.

You need to let this go, or go to 60 minutes.

-@ Scotty, There is something wrong with the transporter, I am still here.

Not all theories can be explained in a few sentences, especially when it involves random sequencing. No one is questioning the integrity of the RNG, the questioning is within deck distribution and the anomaly caused by timing decks, rather than the unified shuffling of a single deck per table.

I am certainly not confused, and I prefer science forums rather than 60 minutes. I can not let this go when there is an obvious problem incurred by process. An obvious problem that is unseen and not thought of to be a problem.

I understand all the sites believe there sites are fare, it is a complex issue that I am trying to discuss on a science forum.

Discussing just aces is nothing, somewhere amongst 1,000,000 decks is 18% of losing aces, somewhere amongst those 1,000,000 decks is game ending coolers,

you can never win a MTT unless you time good decks in the later stages, you can enter a sunday storm and sit there folding 73 type hands for 3 hrs, I did this sunday to only get blind pressure outed of the tourney.

Uneven is not good....

out of 1 million random decks of cards, what are the odds of receiving a game winning cooler hand at the exact time you need it?